Преподавател(и):

проф. Иван Ланджев  д.н.

Описание на курса:

Компетенции:

Gaussian elimination as a basic tool for solving homogeneous and non-homogeneous linear systems of equations

Finding and presenting in different forms the general solution of a system of linear equations; Giving geometrical interpretation of the set of all solutions

Working with matrices; Representation of a matrix as a product of a lower-triangular and upper-triangular matrix; Calculation of inverse matrix; Finding the Rank of a matrix, the dimension and a basis for a given vector space;

Scalar (inner) product of two vectors; Orthogonal vectors and subspaces;

Предварителни изисквания:

Elementary mathematics (school level);

Desire for self-standing work on Home-works and Assignments given during classes

Форми на провеждане:
Редовен

Учебни форми:
Упражнения

Език, на който се води курса:
Английски

Теми, които се разглеждат в курса:

Solving systems of linear equations (homogeneous and non-homogeneous) by Gaussian Elimination;

Representing in different forms the general solution of a system of linear equations;

Vectors and matrices; Product of matrix and a vector, product of two matrices; Representation of Gaussian elimination steps as a sequence of multiplication of a matrix by elementary matrices; Permutations of matrix rows as multiplication of matrices; Representation of a matrix as a product of two matrices: a lower-triangular one and an upper-triangular one;

Methods for calculation of Inverse matrices;

Rang of a matrix; Dimension and basis of a vector space;

Vector spaces generated by a matrix;

Scalar (inner) product of two vectors;

Orthogonality of vectors and subspaces;

Литература по темите:

Any of the numerous text-books on Linear Algebra could be of help.

Preferred book:

Gilbert Strang, "Linear Algebra and itsw Applications",

Brooks/Cole, Third Edition,

ISBN 0-15-551005-3

Средства за оценяване:

Home-works and Assignments given every week; Two written Control Works during the term; Written Final Examination at the end of the term;

If Home-work and assignments are regularly handed to the lecturer and if the average mark from the two Control Works is at least 4.5, the student may be exempted from the Final Examination with a final mark equal to the mentioned average